Assistant Professor

Department of Mathematics and Statistics

University of Victoria

Email: goluskin at uvic.ca

My research is in the broad area of applied nonlinear dynamics and incorporates both computation and analysis. Much of my work concerns fluid dynamics, but I also study simpler ordinary and partial differential equations. Recently I have been developing ways to use polynomial optimization to study dynamics, for instance to estimate time averages and other properties of attractors. A lecture for the public relating generally to some of my fluid dynamical research can be found here. I currently have funding for another PhD or MSc student to join my research group; a strong mathematical background and computational skills are required.

MS Applied Mathematics, Columbia University, 2009

BS Applied Mathematics, University of Colorado Boulder, 2007

BS Aerospace Engineering, University of Colorado Boulder, 2007

Hans Oeri (PhD)

Narges Hosseini (MSc)

Mathew Lewis (MSc)

Hannah Swan (undergrad)

Xuchen Wu (undergrad)

Zehan Zheng (undergrad)

- D. Goluskin

*Internally heated convection and Rayleigh–Bénard convection*

Springer. 2016. arXiv, Springer

- B. Wen, D. Goluskin, C. R. Doering

*Steady Rayleigh–Bénard convection between no-slip boundaries*

arXiv,**talk** - F. Fuentes, D. Goluskin, S. Chernyshenko

*Global stability of fluid flows despite transient growth of energy*

arXiv

- B. Wen, D. Goluskin, M. LeDuc, G. P. Chini, C. R. Doering

*Steady Rayleigh–Bénard convection between stress-free boundaries*

J. Fluid Mech. Rapids 905, R4. 2020. arXiv, JFM - M. Olson, D. Goluskin, W. W. Schultz, C. R. Doering

*Heat transport bounds for a truncated model of Rayleigh–Bénard convection via polynomial optimization*

Physica D 415, 132748. 2020. arXiv, Physica D - J. J. Bramburger, D. Goluskin

*Minimum wave speeds in monostable reaction–diffusion equations: sharp bounds by polynomial optimization*

Proc. R. Soc. A 476, 20200450. 2020. arXiv, Proc A - G. Fantuzzi, D. Goluskin

*Bounding extreme events in nonlinear dynamics using convex optimization*

SIAM J. Appl. Dyn. Syst. 19, 1823-1864. 2020. arXiv, SIADS - D. Goluskin

*Bounding extrema over global attractors using polynomial optimization*

Nonlinearity 33, 4878-4899. 2020 arXiv, Nonlinearity - D. Goluskin, G. Fantuzzi

*Bounds on mean energy in the Kuramoto–Sivashinsky equation computed using semidefinite programming*

Nonlinearity 32, 1705-1730. 2019. arXiv, Nonlinearity - D. Goluskin

*Bounding averages rigorously using semidefinite programming: mean moments of the Lorenz system*

J. Nonlinear Sci. 28, 621-651. 2018. arXiv, JNLS - I. Tobasco, D. Goluskin, C. R. Doering

*Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems*

Phys. Lett. A 382, 382-386. 2018. arXiv, PLA - G. Fantuzzi, D. Goluskin, D. Huang, S. I. Chernyshenko

*Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization*

SIAM J. Appl. Dyn. Syst. 15, 1962-1988. 2016. arXiv, SIADS (open access) - D. Goluskin, C. R. Doering

*Bounds for convection between rough boundaries*

J. Fluid Mech. 804, 370-386. 2016. arXiv, JFM - D. Goluskin, E. P. van der Poel

*Penetrative internally heated convection in two and three dimensions*

J. Fluid Mech. Rapids 791, R6. 2016. arXiv, JFM - J. von Hardenberg, D. Goluskin, A. Provenzale, E. A. Spiegel

*Generation of large-scale winds in horizontally anisotropic convection*

Phys. Rev. Lett. 115, 134501. 2015. arXiv, PRL - D. Goluskin

*Internally heated convection beneath a poor conductor*

J. Fluid Mech. 771, 36-56. 2015. arXiv, JFM - D. Goluskin, H. Johnston, G. R. Flierl, E. A. Spiegel

*Convectively driven shear and decreased heat flux*

J. Fluid Mech. 759, 360-385. 2014. arXiv, videos, JFM - D. Goluskin, E. A. Spiegel

*Convection driven by internal heating*

Phys. Lett. A 377, 83-92. 2012. arXiv, PLA

- D. Goluskin

*Who ate whom: population dynamics with age-structured predation*

in WHOI GFD 2010 program of study: swimming and swirling in turbulence. 2010.

- D. Goluskin

Review of*Exploring ODEs. By Lloyd N. Trefethen, Ásgeir Birkisson, and Tobin A. Driscoll*

SIAM Rev. 61, 392-393. 2019.

- D. Goluskin

*Zonal flow driven by convection and convection driven by internal heating*

Columbia University. 2013. download